A mass \(\mathrm{m}\) is suspended from a spring of negligible mass and the system oscillates with a frequency \(f_1\). The frequency of oscillations if a mass \(9 \mathrm{~m}\) is suspended from the same spring is \(f_2\). The value of \(\frac{f_1}{f_{.2}}\) is _______.

A circular hole of radius \(\frac{R}{4}\) is made in a thin uniform disc having mass \(M\) and radius \(R\), as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point \(O\) and perpendicular to the plane of the disc is

The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of \(5 \times 10^{-4}\) is \(\dots \; kJ / m ^{3}\). Assume that material is elastic upto the linear strain of \(5 \times 10^{-4}\).

In Young's double slit experiment, the distance between slits and the screen is \(1 .0\,\,m\) and monochromatic light of \(600\,\,nm\)  is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance \(d_0\) between the slits . If the angular resolution of the eye is \(\frac {1}{60}^o,\) the value of \(d_0\)  is close to......\(mm\)

A person of \(80\, kg\) mass is standing on the rim of a circular platform of mass \(200\, kg\) rotating about its axis as \(5\) revolutions per minute \((rpm).\) The person now starts moving towards the centre of the platform. What will be the rotational speed (in \(rpm\) ) of the platform when the person reaches its centre \(......rpm\)

The electrostatic potential in a charged spherical region of radius \(r\) varies as \(V=a r^3+b\), where \(a\) and b are constants. The total charge in the sphere of unit radius is \(\alpha \times \pi a \in_0\). The value of \(\alpha\) is _________ .

Mobility of electron in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an \(n-\) type semiconductor, the density of electrons is \(10^{19}\, m^{-3}\) and their mobility is \(1.6\, m^2\,/(V.s)\) then the resistivity of the semiconductor(since it is an \(n-\) type semiconductor contribution of holes is ignored) is close to ................ \(\Omega  m\)

The radius of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm. The refractive index of the lens material is :

In a Young's double slit experiment, a laser light of \(560\,nm\) produces an interference pattern with consecutive bright fringes' separation of \(7.2\,mm\). Now another light is used to produce an interference pattern with consecutive bright fringes' separation of \(8.1\,mm\). The wavelength of second light is \(......nm\)